Abstract algebra I combines many details learned in the earlier stages of mathematics. Matrices, polynomials, vector spaces, modular arithmetic, and more are classified into theoretical ideas called algebraic structures, as well as set theory and group theory. Abstract algebra gives information about the details of symmetries. These features are mostly related to group theory. Abstract algebra gives us the ability to gain new insights about other subjects. The main aim is to obtain groups, subgroups and normal subgroups distributed within the abstract algebras of all these, to make students understand the isomorphism theorems and to be able to use this algebraic structure.

Preliminaries, Groups. Subgroups. Homomorphism. Cyclic Groups. Cosets and its Properties. Normal Subgroups, Quotient Groups, Isomorphism Theorems, Permutation Groups, Cartesian Product of Groups. Sylow Theorems. Classificaton os some small groups of order p, p^2, pq where p and q are primes